Introducing Quantum Ricci Curvature

Motivated by the search for geometric observables in nonperturbative quantum gravity, we define a notion of coarse-grained Ricci curvature. It is based on a particular way of extracting the local Ricci curvature of a smooth Riemannian manifold by comparing the distance between pairs of spheres with that of their centres. The quantum Ricci curvature is designed for use on non-smooth and discrete metric spaces, and to satisfy the key criteria of scalability and computability. We test the prescription on a variety of regular and random piecewise flat spaces, mostly in two dimensions. This enables us to quantify its behaviour for short lattices distances and compare its large-scale behaviour with that of constantly curved model spaces. On the triangulated spaces considered, the quantum Ricci curvature has good averaging properties and reproduces classical characteristics on scales large compared to the discretization scale.Comment: 43 pages, 27 figure

High-Performance and Tunable Stereo Reconstruction

Traditional stereo algorithms have focused their efforts on reconstruction quality and have largely avoided prioritizing for run time performance. Robots, on the other hand, require quick maneuverability and effective computation to observe its immediate environment and perform tasks within it. In this work, we propose a high-performance and tunable stereo disparity estimation method, with a peak frame-rate of 120Hz (VGA resolution, on a single CPU-thread), that can potentially enable robots to quickly reconstruct their immediate surroundings and maneuver at high-speeds. Our key contribution is a disparity estimation algorithm that iteratively approximates the scene depth via a piece-wise planar mesh from stereo imagery, with a fast depth validation step for semi-dense reconstruction. The mesh is initially seeded with sparsely matched keypoints, and is recursively tessellated and refined as needed (via a resampling stage), to provide the desired stereo disparity accuracy. The inherent simplicity and speed of our approach, with the ability to tune it to a desired reconstruction quality and runtime performance makes it a compelling solution for applications in high-speed vehicles.Comment: Accepted to International Conference on Robotics and Automation (ICRA) 2016; 8 pages, 5 figure

Sparse optical flow regularisation for real-time visual tracking

Optical flow can greatly improve the robustness of visual tracking algorithms. While dense optical flow algorithms have various applications, they can not be used for real-time solutions without resorting to GPU calculations. Furthermore, most optical flow algorithms fail in challenging lighting environments due to the violation of the brightness constraint. We propose a simple but effective iterative regularisation scheme for real-time, sparse optical flow algorithms, that is shown to be robust to sudden illumination changes and can handle large displacements. The algorithm proves to outperform well known techniques in real life video sequences, while being much faster to calculate. Our solution increases the robustness of a real-time particle filter based tracking application, consuming only a fraction of the available CPU power. Furthermore, a new and realistic optical flow dataset with annotated ground truth is created and made freely available for research purposes

Automated 3D Scenes Reconstruction Using Multiple Stereo Pairs from Portable Four-Camera Photographic Measurement System

An effective automatic 3D reconstruction method using a portable four-camera photographic measurement system (PFCPMS) is proposed. By taking advantage of the complementary stereo information from four cameras, a fast and highly accurate feature point matching algorithm is developed for 3D reconstruction. Specifically, we first utilize a projection method to obtain a large number of dense feature points. And then a reduction and clustering treatment is applied to simplify the Delaunay triangulation process and reconstruct a 3D model for each scene. In addition, a 3D model stitching approach is proposed to further improve the performance of the limited field-of-view for image-based method. The experimental results tested on the 172 cave in Mogao Grottoes indicate that the proposed method is effective to reconstruct a 3D scene with a low-cost four-camera photographic measurement system

Structural graph matching using the EM algorithm and singular value decomposition

This paper describes an efficient algorithm for inexact graph matching. The method is purely structural, that is, it uses only the edge or connectivity structure of the graph and does not draw on node or edge attributes. We make two contributions: 1) commencing from a probability distribution for matching errors, we show how the problem of graph matching can be posed as maximum-likelihood estimation using the apparatus of the EM algorithm; and 2) we cast the recovery of correspondence matches between the graph nodes in a matrix framework. This allows one to efficiently recover correspondence matches using the singular value decomposition. We experiment with the method on both real-world and synthetic data. Here, we demonstrate that the method offers comparable performance to more computationally demanding method

Efficient Fuzzy Set Theoretic Approach to Image Corner Matching

Corner matching in digital images is a key step in several applications in computer vision such as motion estimation, object recognition and localization, 3D reconstruction etc. Accuracy and reliability of corner matching algorithms are two important criteria. In this paper, corner correspondence between two images is established in the presence of intensity variations, inherent noise and motion blur using a fuzzy set theoretic similarity measure. The proposed matching algorithm needs to extract set of corner points as candidates from both the frames. Fuzzy set theoretic similarity measure is used here as fuzzy logic is a powerful tool which is able to deal with ambiguous data. Experimental results conducted with the help of various test images show that the proposed approach is superior compared existing corner matching algorithms (conventional and recent) considered in this paper under non-ideal conditions. DOI: 10.17762/ijritcc2321-8169.15021